Sparse extended mean-variance-CVaR portfolios with short-selling

Abstract This paper introduces a novel penalty decomposition algorithm customized for addressing the non-differentiable and nonconvex problem of extended mean-variance-CVaR portfolio optimization with short-selling and cardinality constraints. The proposed algorithm solves a sequence of penalty subproblems using a block coordinate descent (BCD) method while striving to fully exploit each component within the objective function and constraints. Through rigorous analysis, the well-posedness of each subproblem of the BCD method is established, and closed-form solutions are derived where possible. A comprehensive theoretical convergence analysis is provided to confirm the efficacy of the introduced algorithm in reaching a Lu–Zhang minimizer for this intractable optimization problem. Numerical experiments conducted on real-world datasets validate the practical applicability and effectiveness of the introduced algorithm based on various criteria. Notably, the existence of closed-form solutions within the BCD subproblems prominently underscores the efficiency of our algorithm when compared to state-of-the-art methods.